No-go results on emergent space and other structures

Abstract It is often claimed that, from the abstract quantum state vector and Hamiltonian, everything emerges uniquely (for example 3D-space, a preferred factorization of Hilbert space, basis). This thesis, called Hilbert-Space Fundamentalism (HSF), assumed for in Carroll Singh’s “Mad-dog Everettianism”, some proposals based on decoherence, that aim to describe by structure alone, spacetime purely theory gravity. I show whenever factorization, or any other like this, there are infinitely many solutions. refutes Fundamentalism. Implications various research programs aiming certain structures emerge uniquely, interpretations Quantum Mechanics, discussed.